Most communications networks are designed to convey multiple communications simultaneously over each individual communication path, for example, a radio frequency (RF) channel or physical connection, using some type of modulation. In recent years, an increasing demand has arisen for efficient and reliable digital data transfers which assure correct data transmissions at as great a data rate as possible. Forward error correction (FEC) codes have been used in some communications systems for this purpose.
Codes are essentially digital data sequences derived from message sequences and used to convey message information. In forward error correction (FEC), information may be encoded to provide the abilities of detection and/or correction of errors occurring in a transmission, for example resulting from a noisy channel. The receiver in a communication system can recover all the information in the codewords by itself and thus coding lends advantages to high speed communication systems and/or those requiring synchronous communications.
Low Density Parity Check (LDPC) codes are a type of FEC block codes which are constructed using a number of simple parity-check relationships shared between the bits in a codeword. An LDPC code (n, k) where n is codeword length and k is the information length, is usually represented by a sparse parity-check matrix H with dimension n*(n−k). The parity check matrix is used as a basis for encoding and decoding LDPC codewords. LDPC codes are well known for their excellent performance in communications systems but due to their block nature, they have thus far not been flexible enough for systems where either information length or codeword length (or both) is variable. Thus a more flexible LDPC coding scheme is desirable.